EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERN-PH-EP-2012-302 LHCb-PAPER-2012-021 October 15, 2012
Measurement of the CP asymmetry
in B
0
→ K
∗0
µ
+
µ
−
decays
The LHCb collaboration†
Abstract
A measurement of the CP asymmetry in B0→ K∗0µ+µ−decays is presented, based
on 1.0 fb−1 of pp collision data recorded by the LHCb experiment during 2011. The measurement is performed in six bins of invariant mass squared of the µ+µ− pair, excluding the J/ψ and ψ(2S) resonance regions. Production and detection asymme-tries are removed using the B0 → J/ψK∗0decay as a control mode. The integrated CP asymmetry is found to be −0.072 ± 0.040 (stat.) ± 0.005 (syst.), consistent with the Standard Model.
Submitted to Physical Review Letters
†Authors are listed on the following pages.
LHCb collaboration
R. Aaij38, C. Abellan Beteta33,n, A. Adametz11, B. Adeva34, M. Adinolfi43, C. Adrover6, A. Affolder49, Z. Ajaltouni5, J. Albrecht35, F. Alessio35, M. Alexander48, S. Ali38,
G. Alkhazov27, P. Alvarez Cartelle34, A.A. Alves Jr22, S. Amato2, Y. Amhis36,
L. Anderlini17,f, J. Anderson37, R.B. Appleby51, O. Aquines Gutierrez10, F. Archilli18,35,
A. Artamonov32, M. Artuso53, E. Aslanides6, G. Auriemma22,m, S. Bachmann11, J.J. Back45, C. Baesso54, V. Balagura36,28, W. Baldini16, R.J. Barlow51, C. Barschel35, S. Barsuk7,
W. Barter44, A. Bates48, Th. Bauer38, A. Bay36, J. Beddow48, I. Bediaga1, S. Belogurov28,
K. Belous32, I. Belyaev28, E. Ben-Haim8, M. Benayoun8, G. Bencivenni18, S. Benson47, J. Benton43, A. Berezhnoy29, R. Bernet37, M.-O. Bettler44, M. van Beuzekom38, A. Bien11, S. Bifani12, T. Bird51, A. Bizzeti17,h, P.M. Bjørnstad51, T. Blake35, F. Blanc36, C. Blanks50,
J. Blouw11, S. Blusk53, A. Bobrov31, V. Bocci22, A. Bondar31, N. Bondar27, W. Bonivento15, S. Borghi48,51, A. Borgia53, T.J.V. Bowcock49, C. Bozzi16, T. Brambach9, J. van den Brand39, J. Bressieux36, D. Brett51, M. Britsch10, T. Britton53, N.H. Brook43, H. Brown49,
A. B¨uchler-Germann37, I. Burducea26, A. Bursche37, J. Buytaert35, S. Cadeddu15, O. Callot7, M. Calvi20,j, M. Calvo Gomez33,n, A. Camboni33, P. Campana18,35, A. Carbone14,c,
G. Carboni21,k, R. Cardinale19,i, A. Cardini15, L. Carson50, K. Carvalho Akiba2, G. Casse49, M. Cattaneo35, Ch. Cauet9, M. Charles52, Ph. Charpentier35, P. Chen3,36, N. Chiapolini37, M. Chrzaszcz 23, K. Ciba35, X. Cid Vidal34, G. Ciezarek50, P.E.L. Clarke47, M. Clemencic35, H.V. Cliff44, J. Closier35, C. Coca26, V. Coco38, J. Cogan6, E. Cogneras5, P. Collins35,
A. Comerma-Montells33, A. Contu52,15, A. Cook43, M. Coombes43, G. Corti35, B. Couturier35, G.A. Cowan36, D. Craik45, S. Cunliffe50, R. Currie47, C. D’Ambrosio35, P. David8,
P.N.Y. David38, I. De Bonis4, K. De Bruyn38, S. De Capua21,k, M. De Cian37, J.M. De Miranda1, L. De Paula2, P. De Simone18, D. Decamp4, M. Deckenhoff9,
H. Degaudenzi36,35, L. Del Buono8, C. Deplano15, D. Derkach14, O. Deschamps5, F. Dettori39, J. Dickens44, H. Dijkstra35, P. Diniz Batista1, F. Domingo Bonal33,n, S. Donleavy49,
F. Dordei11, A. Dosil Su´arez34, D. Dossett45, A. Dovbnya40, F. Dupertuis36, R. Dzhelyadin32, A. Dziurda23, A. Dzyuba27, S. Easo46, U. Egede50, V. Egorychev28, S. Eidelman31,
D. van Eijk38, F. Eisele11, S. Eisenhardt47, R. Ekelhof9, L. Eklund48, I. El Rifai5,
Ch. Elsasser37, D. Elsby42, D. Esperante Pereira34, A. Falabella14,e, C. F¨arber11, G. Fardell47, C. Farinelli38, S. Farry12, V. Fave36, V. Fernandez Albor34, F. Ferreira Rodrigues1,
M. Ferro-Luzzi35, S. Filippov30, C. Fitzpatrick35, M. Fontana10, F. Fontanelli19,i, R. Forty35, O. Francisco2, M. Frank35, C. Frei35, M. Frosini17,f, S. Furcas20, A. Gallas Torreira34, D. Galli14,c, M. Gandelman2, P. Gandini52, Y. Gao3, J-C. Garnier35, J. Garofoli53, J. Garra Tico44, L. Garrido33, C. Gaspar35, R. Gauld52, E. Gersabeck11, M. Gersabeck35, T. Gershon45,35, Ph. Ghez4, V. Gibson44, V.V. Gligorov35, C. G¨obel54, D. Golubkov28, A. Golutvin50,28,35, A. Gomes2, H. Gordon52, M. Grabalosa G´andara33, R. Graciani Diaz33, L.A. Granado Cardoso35, E. Graug´es33, G. Graziani17, A. Grecu26, E. Greening52,
S. Gregson44, O. Gr¨unberg55, B. Gui53, E. Gushchin30, Yu. Guz32, T. Gys35,
C. Hadjivasiliou53, G. Haefeli36, C. Haen35, S.C. Haines44, S. Hall50, T. Hampson43, S. Hansmann-Menzemer11, N. Harnew52, S.T. Harnew43, J. Harrison51, P.F. Harrison45, T. Hartmann55, J. He7, V. Heijne38, K. Hennessy49, P. Henrard5, J.A. Hernando Morata34,
E. van Herwijnen35, E. Hicks49, D. Hill52, M. Hoballah5, P. Hopchev4, W. Hulsbergen38, P. Hunt52, T. Huse49, N. Hussain52, R.S. Huston12, D. Hutchcroft49, D. Hynds48,
E. Jans38, F. Jansen38, P. Jaton36, B. Jean-Marie7, F. Jing3, M. John52, D. Johnson52, C.R. Jones44, B. Jost35, M. Kaballo9, S. Kandybei40, M. Karacson35, M. Karbach35,
J. Keaveney12, I.R. Kenyon42, U. Kerzel35, T. Ketel39, A. Keune36, B. Khanji20, Y.M. Kim47,
O. Kochebina7, I. Komarov29, V. Komarov36, R.F. Koopman39, P. Koppenburg38, M. Korolev29, A. Kozlinskiy38, L. Kravchuk30, K. Kreplin11, M. Kreps45, G. Krocker11, P. Krokovny31, F. Kruse9, M. Kucharczyk20,23,j, V. Kudryavtsev31, T. Kvaratskheliya28,35,
V.N. La Thi36, D. Lacarrere35, G. Lafferty51, A. Lai15, D. Lambert47, R.W. Lambert39, E. Lanciotti35, G. Lanfranchi18,35, C. Langenbruch35, T. Latham45, C. Lazzeroni42, R. Le Gac6, J. van Leerdam38, J.-P. Lees4, R. Lef`evre5, A. Leflat29,35, J. Lefran¸cois7,
O. Leroy6, T. Lesiak23, L. Li3, Y. Li3, L. Li Gioi5, M. Liles49, R. Lindner35, C. Linn11, B. Liu3, G. Liu35, J. von Loeben20, J.H. Lopes2, E. Lopez Asamar33, N. Lopez-March36, H. Lu3,
J. Luisier36, A. Mac Raighne48, F. Machefert7, I.V. Machikhiliyan4,28, F. Maciuc26, O. Maev27,35, J. Magnin1, M. Maino20, S. Malde52, G. Manca15,d, G. Mancinelli6, N. Mangiafave44, U. Marconi14, R. M¨arki36, J. Marks11, G. Martellotti22, A. Martens8, L. Martin52, A. Mart´ın S´anchez7, M. Martinelli38, D. Martinez Santos35, A. Massafferri1, Z. Mathe35, C. Matteuzzi20, M. Matveev27, E. Maurice6, A. Mazurov16,30,35, J. McCarthy42, G. McGregor51, R. McNulty12, M. Meissner11, M. Merk38, J. Merkel9, D.A. Milanes13, M.-N. Minard4, J. Molina Rodriguez54, S. Monteil5, D. Moran51, P. Morawski23,
R. Mountain53, I. Mous38, F. Muheim47, K. M¨uller37, R. Muresan26, B. Muryn24, B. Muster36, J. Mylroie-Smith49, P. Naik43, T. Nakada36, R. Nandakumar46, I. Nasteva1, M. Needham47, N. Neufeld35, A.D. Nguyen36, C. Nguyen-Mau36,o, M. Nicol7, V. Niess5, N. Nikitin29,
T. Nikodem11, A. Nomerotski52,35, A. Novoselov32, A. Oblakowska-Mucha24, V. Obraztsov32, S. Oggero38, S. Ogilvy48, O. Okhrimenko41, R. Oldeman15,d,35, M. Orlandea26,
J.M. Otalora Goicochea2, P. Owen50, B.K. Pal53, A. Palano13,b, M. Palutan18, J. Panman35, A. Papanestis46, M. Pappagallo48, C. Parkes51, C.J. Parkinson50, G. Passaleva17, G.D. Patel49, M. Patel50, G.N. Patrick46, C. Patrignani19,i, C. Pavel-Nicorescu26, A. Pazos Alvarez34,
A. Pellegrino38, G. Penso22,l, M. Pepe Altarelli35, S. Perazzini14,c, D.L. Perego20,j,
E. Perez Trigo34, A. P´erez-Calero Yzquierdo33, P. Perret5, M. Perrin-Terrin6, G. Pessina20, K. Petridis50, A. Petrolini19,i, A. Phan53, E. Picatoste Olloqui33, B. Pie Valls33, B. Pietrzyk4, T. Pilaˇr45, D. Pinci22, S. Playfer47, M. Plo Casasus34, F. Polci8, G. Polok23, A. Poluektov45,31, E. Polycarpo2, D. Popov10, B. Popovici26, C. Potterat33, A. Powell52, J. Prisciandaro36,
V. Pugatch41, A. Puig Navarro36, W. Qian3, J.H. Rademacker43, B. Rakotomiaramanana36, M.S. Rangel2, I. Raniuk40, N. Rauschmayr35, G. Raven39, S. Redford52, M.M. Reid45, A.C. dos Reis1, S. Ricciardi46, A. Richards50, K. Rinnert49, V. Rives Molina33,
D.A. Roa Romero5, P. Robbe7, E. Rodrigues48,51, P. Rodriguez Perez34, G.J. Rogers44, S. Roiser35, V. Romanovsky32, A. Romero Vidal34, J. Rouvinet36, T. Ruf35, H. Ruiz33, G. Sabatino21,k, J.J. Saborido Silva34, N. Sagidova27, P. Sail48, B. Saitta15,d, C. Salzmann37,
B. Sanmartin Sedes34, M. Sannino19,i, R. Santacesaria22, C. Santamarina Rios34, R. Santinelli35, E. Santovetti21,k, M. Sapunov6, A. Sarti18,l, C. Satriano22,m, A. Satta21, M. Savrie16,e, D. Savrina28, P. Schaack50, M. Schiller39, H. Schindler35, S. Schleich9,
M. Schlupp9, M. Schmelling10, B. Schmidt35, O. Schneider36, A. Schopper35, M.-H. Schune7, R. Schwemmer35, B. Sciascia18, A. Sciubba18,l, M. Seco34, A. Semennikov28, K. Senderowska24, I. Sepp50, N. Serra37, J. Serrano6, P. Seyfert11, M. Shapkin32, I. Shapoval40,35, P. Shatalov28, Y. Shcheglov27, T. Shears49,35, L. Shekhtman31, O. Shevchenko40, V. Shevchenko28,
A. Shires50, R. Silva Coutinho45, T. Skwarnicki53, N.A. Smith49, E. Smith52,46, M. Smith51, K. Sobczak5, F.J.P. Soler48, A. Solomin43, F. Soomro18,35, D. Souza43, B. Souza De Paula2,
B. Spaan9, A. Sparkes47, P. Spradlin48, F. Stagni35, S. Stahl11, O. Steinkamp37, S. Stoica26, S. Stone53, B. Storaci38, M. Straticiuc26, U. Straumann37, V.K. Subbiah35, S. Swientek9, M. Szczekowski25, P. Szczypka36,35, T. Szumlak24, S. T’Jampens4, M. Teklishyn7,
E. Teodorescu26, F. Teubert35, C. Thomas52, E. Thomas35, J. van Tilburg11, V. Tisserand4, M. Tobin37, S. Tolk39, S. Topp-Joergensen52, N. Torr52, E. Tournefier4,50, S. Tourneur36, M.T. Tran36, A. Tsaregorodtsev6, N. Tuning38, M. Ubeda Garcia35, A. Ukleja25, D. Urner51,
U. Uwer11, V. Vagnoni14, G. Valenti14, R. Vazquez Gomez33, P. Vazquez Regueiro34, S. Vecchi16, J.J. Velthuis43, M. Veltri17,g, G. Veneziano36, M. Vesterinen35, B. Viaud7,
I. Videau7, D. Vieira2, X. Vilasis-Cardona33,n, J. Visniakov34, A. Vollhardt37, D. Volyanskyy10, D. Voong43, A. Vorobyev27, V. Vorobyev31, H. Voss10, C. Voß55, R. Waldi55, R. Wallace12, S. Wandernoth11, J. Wang53, D.R. Ward44, N.K. Watson42, A.D. Webber51, D. Websdale50, M. Whitehead45, J. Wicht35, D. Wiedner11, L. Wiggers38, G. Wilkinson52, M.P. Williams45,46, M. Williams50,p, F.F. Wilson46, J. Wishahi9, M. Witek23,35, W. Witzeling35, S.A. Wotton44, S. Wright44, S. Wu3, K. Wyllie35, Y. Xie47, F. Xing52, Z. Xing53, Z. Yang3, R. Young47, X. Yuan3, O. Yushchenko32, M. Zangoli14, M. Zavertyaev10,a, F. Zhang3, L. Zhang53, W.C. Zhang12, Y. Zhang3, A. Zhelezov11, L. Zhong3, A. Zvyagin35.
1Centro Brasileiro de Pesquisas F´ısicas (CBPF), Rio de Janeiro, Brazil 2Universidade Federal do Rio de Janeiro (UFRJ), Rio de Janeiro, Brazil 3Center for High Energy Physics, Tsinghua University, Beijing, China 4LAPP, Universit´e de Savoie, CNRS/IN2P3, Annecy-Le-Vieux, France
5Clermont Universit´e, Universit´e Blaise Pascal, CNRS/IN2P3, LPC, Clermont-Ferrand, France 6CPPM, Aix-Marseille Universit´e, CNRS/IN2P3, Marseille, France
7LAL, Universit´e Paris-Sud, CNRS/IN2P3, Orsay, France
8LPNHE, Universit´e Pierre et Marie Curie, Universit´e Paris Diderot, CNRS/IN2P3, Paris, France 9Fakult¨at Physik, Technische Universit¨at Dortmund, Dortmund, Germany
10Max-Planck-Institut f¨ur Kernphysik (MPIK), Heidelberg, Germany
11Physikalisches Institut, Ruprecht-Karls-Universit¨at Heidelberg, Heidelberg, Germany 12School of Physics, University College Dublin, Dublin, Ireland
13Sezione INFN di Bari, Bari, Italy 14Sezione INFN di Bologna, Bologna, Italy 15Sezione INFN di Cagliari, Cagliari, Italy 16Sezione INFN di Ferrara, Ferrara, Italy 17Sezione INFN di Firenze, Firenze, Italy
18Laboratori Nazionali dell’INFN di Frascati, Frascati, Italy 19Sezione INFN di Genova, Genova, Italy
20Sezione INFN di Milano Bicocca, Milano, Italy 21Sezione INFN di Roma Tor Vergata, Roma, Italy 22Sezione INFN di Roma La Sapienza, Roma, Italy
23Henryk Niewodniczanski Institute of Nuclear Physics Polish Academy of Sciences, Krak´ow, Poland 24AGH University of Science and Technology, Krak´ow, Poland
25National Center for Nuclear Research (NCBJ), Warsaw, Poland
26Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest-Magurele, Romania 27Petersburg Nuclear Physics Institute (PNPI), Gatchina, Russia
28Institute of Theoretical and Experimental Physics (ITEP), Moscow, Russia
29Institute of Nuclear Physics, Moscow State University (SINP MSU), Moscow, Russia
30Institute for Nuclear Research of the Russian Academy of Sciences (INR RAN), Moscow, Russia 31Budker Institute of Nuclear Physics (SB RAS) and Novosibirsk State University, Novosibirsk, Russia 32Institute for High Energy Physics (IHEP), Protvino, Russia
34Universidad de Santiago de Compostela, Santiago de Compostela, Spain 35European Organization for Nuclear Research (CERN), Geneva, Switzerland 36Ecole Polytechnique F´ed´erale de Lausanne (EPFL), Lausanne, Switzerland 37Physik-Institut, Universit¨at Z¨urich, Z¨urich, Switzerland
38Nikhef National Institute for Subatomic Physics, Amsterdam, The Netherlands
39Nikhef National Institute for Subatomic Physics and VU University Amsterdam, Amsterdam, The
Netherlands
40NSC Kharkiv Institute of Physics and Technology (NSC KIPT), Kharkiv, Ukraine
41Institute for Nuclear Research of the National Academy of Sciences (KINR), Kyiv, Ukraine 42University of Birmingham, Birmingham, United Kingdom
43H.H. Wills Physics Laboratory, University of Bristol, Bristol, United Kingdom 44Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom 45Department of Physics, University of Warwick, Coventry, United Kingdom 46STFC Rutherford Appleton Laboratory, Didcot, United Kingdom
47School of Physics and Astronomy, University of Edinburgh, Edinburgh, United Kingdom 48School of Physics and Astronomy, University of Glasgow, Glasgow, United Kingdom 49Oliver Lodge Laboratory, University of Liverpool, Liverpool, United Kingdom 50Imperial College London, London, United Kingdom
51School of Physics and Astronomy, University of Manchester, Manchester, United Kingdom 52Department of Physics, University of Oxford, Oxford, United Kingdom
53Syracuse University, Syracuse, NY, United States
54Pontif´ıcia Universidade Cat´olica do Rio de Janeiro (PUC-Rio), Rio de Janeiro, Brazil, associated to2 55Institut f¨ur Physik, Universit¨at Rostock, Rostock, Germany, associated to11
aP.N. Lebedev Physical Institute, Russian Academy of Science (LPI RAS), Moscow, Russia bUniversit`a di Bari, Bari, Italy
cUniversit`a di Bologna, Bologna, Italy dUniversit`a di Cagliari, Cagliari, Italy eUniversit`a di Ferrara, Ferrara, Italy fUniversit`a di Firenze, Firenze, Italy gUniversit`a di Urbino, Urbino, Italy
hUniversit`a di Modena e Reggio Emilia, Modena, Italy iUniversit`a di Genova, Genova, Italy
jUniversit`a di Milano Bicocca, Milano, Italy kUniversit`a di Roma Tor Vergata, Roma, Italy lUniversit`a di Roma La Sapienza, Roma, Italy mUniversit`a della Basilicata, Potenza, Italy
nLIFAELS, La Salle, Universitat Ramon Llull, Barcelona, Spain oHanoi University of Science, Hanoi, Viet Nam
The decay B0 → K∗0(→ K+π−)µ+µ− is a flavour changing neutral current process which proceeds via electroweak loop and box diagrams in the Standard Model (SM) [1]. The decay is highly suppressed in the SM and therefore physics beyond the SM such as su-persymmetry [2] can contribute with a comparable amplitude via gluino or chargino loop diagrams. A number of observables are sensitive to such contributions, including the partial rate of the decay, the µ+µ− forward-backward asymmetry (A
FB) and the CP asymmetry (ACP). The CP asymmetry for B0 → K∗0µ+µ− is defined as
ACP =
Γ(B0→ K∗0µ+µ−) − Γ(B0 → K∗0µ+µ−)
Γ(B0→ K∗0µ+µ−) + Γ(B0 → K∗0µ+µ−) (1) where Γ is the decay rate and the initial flavour of the B meson is tagged by the charge of the kaon from the K∗ decay. The CP asymmetry is predicted to be of the order 10−3 in the SM [3, 4], but is sensitive to physics beyond the SM that changes the operator basis by modifying the mixture of the vector and axial-vector components [5, 6]. Some models that include new phenomena enhance the observed CP asymmetry up to ±0.15 [7]. The theoretical prediction within a given model has a small error as the form factor uncertainties, which are the dominant theoretical errors for the decay rate, cancel in the ratio.
The CP asymmetry in B0 → K∗0µ+µ− decays has previously been measured by the Belle [8] and BaBar [9] collaborations, with both results consistent with the SM. The LHCb collaboration has recently demonstrated its potential in this area with the most precise measurement of AFB [10], and in this Letter, the measurement of the CP asym-metry by LHCb is presented.
The LHCb detector [11] is a single-arm forward spectrometer covering the pseudo-rapidity range 2 < η < 5, designed for the study of particles containing b or c quarks. The detector includes a high precision tracking system consisting of a silicon-strip vertex detector surrounding the pp interaction region, a large-area silicon-strip detector located upstream of a dipole magnet with a bending power of about 4 Tm, and three stations of silicon-strip detectors and straw drift-tubes placed downstream. The combined tracking system has a momentum resolution ∆p/p that varies from 0.4% at 5 GeV/c to 0.6% at 100 GeV/c, and an impact parameter (IP) resolution of 20 µm for tracks with high trans-verse momentum (pT). Charged hadrons are identified using two ring-imaging Cherenkov detectors. Photon, electron and hadron candidates are identified by a calorimeter system consisting of scintillating-pad and pre-shower detectors, an electromagnetic calorimeter and a hadronic calorimeter. Muons are identified by a system composed of alternating layers of iron and multiwire proportional chambers. The trigger consists of a hardware stage, based on information from the calorimeter and muon systems, followed by a soft-ware stage which makes use of a full event reconstruction.
The simulated events used in this analysis are produced using the Pythia 6.4 genera-tor [12], with a choice of parameters specifically configured for LHCb [13]. The EvtGen package [14] describes the decay of the particles and the Geant4 toolkit [15] simulates the detector response, implemented as described in Ref. [16]. QED radiative corrections are generated with the Photos package [17].
The events used in the analysis are selected by a dedicated muon hardware trigger and then by one or more of a set of different muon and topological software triggers [18, 19]. The hardware trigger requires the muons have pTgreater than 1.48 GeV/c, and the software trigger requires that one of the final state particles to have both pT > 0.8 GeV/c and IP with respect to all pp interaction vertices > 100 µm [19]. Triggered candidates are subject to the same two-stage selection as that used in Ref. [10]. The first stage is a cut-based selection, which includes requirements on the B0 candidate’s vertex fit χ2, flight distance and invariant mass, and each track’s impact parameters with respect to any interaction vertex, pT and polar angle. Background from misidentified kaon and pion tracks is removed using information from the particle identification (PID) system, and muon tracks are required to have hits in the muon system. Finally, the production vertex of the B0 candidate must lie within 5 mm of the beam axis in the transverse directions, and within 200 mm of the average interaction position in the beam (z) direction.
In the second stage, the candidates must pass a multivariate selection that uses a boosted decision tree (BDT) [20] that implements the AdaBoost algorithm [21]. This is a tighter selection which takes into account other variables including the decay time and flight direction of the B0 candidates, the p
T of the hadrons, measures of the track and vertex quality, and PID information for the daughter tracks. For the rest of the Letter, the inclusion of charge conjugate modes is implied unless explicitly stated.
In order to obtain a clean sample of B0 → K∗0µ+µ− decays, the c¯c resonant decays B0 → J/ψK∗0and B0 → ψ(2S)K∗0are removed by excluding events with µ+µ−invariant mass, mµ+µ−, satisfying 2.95 < mµ+µ− < 3.18 GeV/c2 or 3.59 < mµ+µ− < 3.77 GeV/c2.
If mK+π−µ+µ− < 5.23 GeV/c2, then the vetoes are extended downwards by 0.15 GeV/c2 to
remove the radiative tails of the resonances. Backgrounds involving misidentified particles are vetoed using cuts on the masses of the B0 and K∗0 mesons and the µ+µ− pair, as well as using the PID information for the daughter particles. These include B0
s → φµ+µ − candidates in which a kaon has been misidentified as a pion, B0 → J/ψK∗0 candidates where a hadron is swapped with a muon and B+ → K+µ+µ− candidates which combine with a random low momentum pion. The vetoes are described fully in Ref. [10]. ACP may be diluted by B0 → K∗0µ+µ− candidates with the kaon and pion misidentified as each other, which is estimated as 0.8% of the B0 → K∗0µ+µ− yield using simulated events. All B0 candidates must have a mass in the range 5.15 − 5.80 GeV/c2, the tight low mass edge of this window serves to remove background from partially reconstructed B meson decays. All K∗0 candidates must have an invariant mass of the kaon-pion pair within 0.1 GeV/c2 of the nominal K∗0(892) mass. A proton veto, using PID information from a neural network, is also applied to remove background from Λb decays, where a proton in the final state is misidentified as a kaon or pion in the B0 → K∗0µ+µ− decay.
Approximately 2% of selected events contain two B0 → K∗0µ+µ− candidates which have tracks in common. The majority of these candidates arise from swapping the as-signment of the kaon and pion hypothesis. As the charges of the kaon and pion tag the flavour of the B meson these duplicate candidates can bias the measured value of ACP. This is accounted for by randomly removing one of the two candidates from the sample. This process is repeated many times over the full sample with a different random seed in
each case and the average measured value of ACP is taken as the result.
An accurate measurement of ACP requires that the differences in the production rates (R) of B0/B0 mesons and detection efficiencies () between the B0 → K∗0µ+µ− and B0 → K∗0µ+µ− modes be accounted for. Assuming all asymmetries are small the raw measured asymmetry may be expressed as
ARAW = ACP + κAP+ AD, (2)
where the production asymmetry, which is of the order of 1% [22], is de-fined as AP≡R B0 − R (B0) / R B0 + R (B0)
and the detection asymmetry is AD≡ B0 − (B0) / B0 + (B0). The production asymmetry is diluted through B0-B0 oscillations by a factor κ κ ≡ R∞ 0 (t)e −Γtcos ∆mt dt R∞ 0 (t)e −Γtdt , (3)
where t, Γ, and ∆m are the decay time, mean decay rate, and mass difference between the light and heavy eigenstates of the B0 meson respectively. The quantity AD is dominated by the K+π−/K−π+ detection asymmetry which arises due to left-right asymmetries in the LHCb detector and different interactions of positively and negatively charged tracks with the detector material. The left-right asymmetry is cancelled by taking an average with equal weights of the CP asymmetries measured in two independent data samples with opposite polarities of the LHCb dipole magnet. These data samples correspond to 61% and 39% of the total data sample.
The production and interaction asymmetries are corrected for using the B0 → J/ψK∗0 decay mode as a control channel. Since B0 → K∗0µ+µ− and B0 → J/ψK∗0 decays have the same final state and similar kinematics, the measured raw asymmetry for B → J/ψ K∗0 decays may be simply expressed as ARAW(B0 → J/ψK∗0) = κAP+AD, in the absence of a CP asymmetry. B0 → J/ψK∗0proceeds via a b → ccs transition, as does the decay mode B+→ J/ψ K+, and hence should have a CP asymmetry similar to A
CP(B+→ J/ψ K+) = (1 ± 7) × 10−3 [23, 24]. For this analysis, it is assumed that ACP(B0 → J/ψK∗0) = 0. The CP asymmetry in B0 → K∗0µ+µ− decays is then calculated as
ACP = ARAW B0→ K∗0µ+µ− − ARAW B0 → J/ψK∗0 . (4) Non-cancelling asymmetries due to differences between the kinematics of B0 → K∗0µ+µ− and B0 → J/ψK∗0 decays are considered as systematic effects.
The full data sample, containing approximately 900 B0 → K∗0µ+µ− signal decays, is split into the six bins of µ+µ− invariant mass squared (q2) used by the LHCb, Belle, and CDF angular analyses [8, 10, 25]. An additional bin of 1 < q2 < 6 GeV2/c4 is used, to be compared to the theoretical prediction in Ref. [4]. The B0 → J/ψK∗0 data sample contains approximately 104000 signal decays with 3.04 < q2 < 3.16 GeV2/c4. The values of ACP are measured using a simultaneous unbinned maximum-likelihood fit to the B0 → K∗0µ+µ−and B0 → J/ψK∗0 invariant mass distributions in the range 5.15 − 5.80 GeV/c2. The simultaneous fit in each q2 bin spans eight data samples, split between the initial
particles B0 and B0, the decay modes B0 → K∗0µ+µ− and B0 → J/ψK∗0, and magnet polarity, where the B0 → J/ψK∗0 sample is common to all q2 bins. This fit returns two values of ACP, one for each magnet polarity, and an average with equal weights is made to find the value of ACP in that q2 bin. An integrated value of ACP over all q2 is also calculated.
The signal invariant mass distributions for the B0 → K∗0µ+µ− and B0 → J/ψK∗0 decays are modelled using the sum of two Crystal Ball functions [26] with common peak and tail parameters but different widths. The values of the tail parameters are determined from fits to simulated events and fixed in the fit. Combinatorial background arising from the random misassociation of tracks to form a B0 candidate is modelled using an exponential function. The B0 → J/ψK∗0 fit also accounts for a peaking B0
s → J/ψK ∗0 contribution, which has the same shape as the signal and an expected yield which is (0.7 ± 0.2)% of that of B0 → J/ψK∗0 [27]. In the simultaneous fit, the signal shape is the same for the two modes, but the signal and background yields and the exponential background parameter may vary. Figure 1 shows the mass fit to the B0 → K∗0µ+µ− decay in the full q2 range.
Many sources of systematic uncertainty cancel in the difference of the raw asymmetries between B0 → K∗0µ+µ− and B0 → J/ψK∗0 decays and in the average of CP asymme-tries measured using data recorded with opposite magnet polarities. However, systematic uncertainties can arise from residual non-cancelling asymmetries due to the different kine-matic behaviour of B0 → K∗0µ+µ− and B0 → J/ψK∗0 decays. The effect is estimated by reweighting B0 → J/ψK∗0 candidates so that their kinematic variables are distributed in the same way as for B0 → K∗0µ+µ− candidates. The value of A
RAW(B0 → J/ψK∗0) is then calculated for these reweighted events and the difference from the default value is taken as the systematic uncertainty. This procedure is carried out separately for a num-ber of quantities including the p, pT, and pseudorapidity of the B0 and the K∗0 mesons. The total systematic uncertainty associated to the different kinematic behaviour of the two decays is calculated by adding each individual contribution in quadrature. This is conservative, as many of the variables are correlated.
The random removal of multiple candidates discussed above also introduces a system-atic uncertainty on ACP. The uncertainty on the mean value of ACP from the ten different random removals is taken as the systematic uncertainty.
The forward-backward asymmetry in B0 → K∗0µ+µ− decays [10], which varies as a function of q2, causes positive and negative muons to have different momentum dis-tributions. Different detection efficiencies for positive and negative muons introduce an asymmetry that cannot be accounted for by the B0 → J/ψK∗0 decay, which does not have a comparable forward-backward asymmetry. The selection efficiencies for positive and negative muons are evaluated using muons from J/ψ decay in data and the resulting asymmetry in the selected B0 → K∗0µ+µ− sample is calculated in each q2 bin.
A number of possible effects due to the choice of model for the mass fit are considered. The signal model is replaced with a sum of two Gaussian distributions and a possible difference in the mass resolution for B0 → K∗0µ+µ− and B0 → J/ψK∗0 decays is inves-tigated by allowing the width of the B0 → K∗0µ+µ− signal peak to vary in a range of
] 2 c [GeV/ -µ + µ -π + K m 5.2 5.4 5.6 5.8 ) 2 c Candidates / ( 0.013 GeV/ 0 10 20 30 40 50 60 70
LHCb
(a) ] 2 c [GeV/ -µ + µ + π -K m 5.2 5.4 5.6 5.8 ) 2 c Candidates / ( 0.013 GeV/ 0 10 20 30 40 50 60 70LHCb
(b) ] 2 c [GeV/ -µ + µ -π + K m 5.2 5.4 5.6 5.8 ) 2 c Candidates / ( 0.013 GeV/ 0 10 20 30 40 50 60 70 80 90LHCb
(c) ] 2 c [GeV/ -µ + µ + π -K m 5.2 5.4 5.6 5.8 ) 2 c Candidates / ( 0.013 GeV/ 0 10 20 30 40 50 60 70 80 90LHCb
(d)Figure 1: Mass fits for B0 → K∗0µ+µ− decays used to extract the integrated CP asym-metry. The curves displayed are the full mass fit (blue, solid), the signal peak (red, short-dashed), and the background (grey, long-dashed). The mass fits on the top row correspond to the (a) B0 and (b) B0 decays for one magnet polarity, while the bottom row shows the mass fits for (c) B0 and (d) B0 for the reverse polarity.
0.7−1.3 times that of the B0 → J/ψK∗0 model. As a further cross-check, A
CP is calcu-lated using a weighted average of the measurements from the six q2 bins and the result is found to be consistent with that obtained from the integrated dataset.
The results of the full ACP fit are presented in Table 2 and Figure 2. The raw asym-metry in B0 → J/ψK∗0 decays is measured as
ARAW B0 → J/ψK∗0 = −0.0110 ± 0.0032 ± 0.0006.
where the first uncertainty is statistical and the second is systematic. The CP asymmetry integrated over the full q2 range is calculated and found to be
ACP B0 → K∗0µ+µ− = −0.072 ± 0.040 ± 0.005.
The result is consistent with previous measurements made by Belle [8], ACP (B → K∗l+l−) = −0.10 ± 0.10 ± 0.01, and BaBar [9], A
CP (B → K∗l+l−) = 0.03 ± 0.13 ± 0.01. This measurement is significantly more precise than all other measurements of ACP in B0 → K∗0µ+µ− decays to date.
Table 1: Systematic uncertainties on ACP, from residual kinematic asymmetries, muon asymmetry, choice of signal model, and the modelling of the mass resolution, for each q2 bin. The total uncertainty is calculated by adding the individual uncertainties in quadrature.
Sources of systematic uncertainties
multiple residual µ± detection signal mass
q2 region ( GeV2/c4) cands. asymmetries asymmetry model resol. Total 0.05 < q2 < 2.00 0.002 0.007 0.005 0.005 0.001 0.010 2.00 < q2 < 4.30 0.006 0.007 0.006 0.007 0.010 0.016 4.30 < q2 < 8.68 0.004 0.003 0.006 0.004 0.003 0.010 10.09 < q2 < 12.86 0.003 0.007 0.009 0.001 0.002 0.011 14.18 < q2 < 16.00 0.001 0.006 0.007 0.001 0.001 0.009 16.00 < q2 < 20.00 0.003 0.005 0.003 0.003 0.009 0.012 1.00 < q2 < 6.00 0.001 0.006 0.005 0.002 0.003 0.009 0.05 < q2 < 20.00 0.002 0.002 0.005 0.001 0.001 0.005
Table 2: Values of ACP for B0 → K∗0µ+µ− in the q2 bins used in the analysis.
signal statistical systematic total
q2 region ( GeV2/c4) yield A
CP uncertainty uncertainty uncertainty 0.05 < q2 < 2.00 168±15 −0.196 0.094 0.010 0.095 2.00 < q2 < 4.30 72±11 −0.098 0.153 0.016 0.154 4.30 < q2 < 8.68 266±19 −0.021 0.073 0.010 0.075 10.09 < q2 < 12.86 157±15 −0.054 0.097 0.011 0.098 14.18 < q2 < 16.00 116±12 −0.201 0.104 0.009 0.104 16.00 < q2 < 20.00 128±13 0.089 0.100 0.012 0.101 1.00 < q2 < 6.00 194±17 −0.058 0.064 0.009 0.064 0.05 < q2 < 20.00 904±35 −0.072 0.040 0.005 0.040
]
4c
/
2[GeV
2q
0
5
10
15
20
CP
A
-0.3
-0.2
-0.1
0
0.1
0.2
LHCb
Figure 2: Fitted value of ACP in B0 → K∗0µ+µ− decays in bins of the µ+µ− invariant mass squared (q2). The red vertical lines mark the charmonium vetoes. The points are plotted at the mean value of q2 in each bin. The uncertainties on each ACP value are the statistical and systematic uncertainties added in quadrature. The dashed line corresponds to the q2 integrated value, and the grey band is the 1σ uncertainty on this value.
Acknowledgements
We express our gratitude to our colleagues in the CERN accelerator departments for the excellent performance of the LHC. We thank the technical and administrative staff at the LHCb institutes. We acknowledge support from CERN and from the national agencies: CAPES, CNPq, FAPERJ and FINEP (Brazil); NSFC (China); CNRS/IN2P3 and Re-gion Auvergne (France); BMBF, DFG, HGF and MPG (Germany); SFI (Ireland); INFN (Italy); FOM and NWO (The Netherlands); SCSR (Poland); ANCS/IFA (Romania); MinES, Rosatom, RFBR and NRC “Kurchatov Institute” (Russia); MinECo, XuntaGal and GENCAT (Spain); SNSF and SER (Switzerland); NAS Ukraine (Ukraine); STFC (United Kingdom); NSF (USA). We also acknowledge the support received from the ERC under FP7. The Tier1 computing centres are supported by IN2P3 (France), KIT and BMBF (Germany), INFN (Italy), NWO and SURF (The Netherlands), CIEMAT, IFAE and UAB (Spain), GridPP (United Kingdom). We are thankful for the computing re-sources put at our disposal by Yandex LLC (Russia), as well as to the communities behind the multiple open source software packages that we depend on.
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